Properties

Label 720.2.u.a.179.11
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.11
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.04776 - 0.949842i) q^{2} +(0.195601 + 1.99041i) q^{4} +(0.469629 - 2.18619i) q^{5} +2.94937i q^{7} +(1.68563 - 2.27126i) q^{8} +O(q^{10})\) \(q+(-1.04776 - 0.949842i) q^{2} +(0.195601 + 1.99041i) q^{4} +(0.469629 - 2.18619i) q^{5} +2.94937i q^{7} +(1.68563 - 2.27126i) q^{8} +(-2.56860 + 1.84453i) q^{10} +(-3.81783 + 3.81783i) q^{11} +(0.772847 - 0.772847i) q^{13} +(2.80143 - 3.09023i) q^{14} +(-3.92348 + 0.778653i) q^{16} +2.27916 q^{17} +(-5.18129 + 5.18129i) q^{19} +(4.44329 + 0.507134i) q^{20} +(7.62651 - 0.373835i) q^{22} -2.63370 q^{23} +(-4.55890 - 2.05340i) q^{25} +(-1.54384 + 0.0756756i) q^{26} +(-5.87045 + 0.576899i) q^{28} +(-3.25626 + 3.25626i) q^{29} -1.93666i q^{31} +(4.85046 + 2.91084i) q^{32} +(-2.38802 - 2.16484i) q^{34} +(6.44789 + 1.38511i) q^{35} +(2.66367 + 2.66367i) q^{37} +(10.3501 - 0.507341i) q^{38} +(-4.17380 - 4.75178i) q^{40} +1.01630 q^{41} +(-4.46535 + 4.46535i) q^{43} +(-8.34584 - 6.85229i) q^{44} +(2.75948 + 2.50160i) q^{46} -6.93871i q^{47} -1.69876 q^{49} +(2.82622 + 6.48170i) q^{50} +(1.68945 + 1.38711i) q^{52} +(-9.01752 + 9.01752i) q^{53} +(6.55356 + 10.1395i) q^{55} +(6.69879 + 4.97155i) q^{56} +(6.50472 - 0.318847i) q^{58} +(-2.82309 + 2.82309i) q^{59} +(10.8603 + 10.8603i) q^{61} +(-1.83952 + 2.02916i) q^{62} +(-2.31728 - 7.65704i) q^{64} +(-1.32664 - 2.05255i) q^{65} +(7.21414 + 7.21414i) q^{67} +(0.445807 + 4.53647i) q^{68} +(-5.44020 - 7.57574i) q^{70} +8.03085i q^{71} +1.58003 q^{73} +(-0.260821 - 5.32095i) q^{74} +(-11.3264 - 9.29943i) q^{76} +(-11.2602 - 11.2602i) q^{77} +0.288222i q^{79} +(-0.140294 + 8.94317i) q^{80} +(-1.06484 - 0.965323i) q^{82} +(8.90062 - 8.90062i) q^{83} +(1.07036 - 4.98270i) q^{85} +(8.91999 - 0.437238i) q^{86} +(2.23584 + 15.1068i) q^{88} -6.44258 q^{89} +(2.27941 + 2.27941i) q^{91} +(-0.515154 - 5.24214i) q^{92} +(-6.59067 + 7.27010i) q^{94} +(8.89402 + 13.7606i) q^{95} -18.1267i q^{97} +(1.77989 + 1.61355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04776 0.949842i −0.740878 0.671640i
\(3\) 0 0
\(4\) 0.195601 + 1.99041i 0.0978005 + 0.995206i
\(5\) 0.469629 2.18619i 0.210025 0.977696i
\(6\) 0 0
\(7\) 2.94937i 1.11476i 0.830259 + 0.557378i \(0.188193\pi\)
−0.830259 + 0.557378i \(0.811807\pi\)
\(8\) 1.68563 2.27126i 0.595962 0.803013i
\(9\) 0 0
\(10\) −2.56860 + 1.84453i −0.812262 + 0.583293i
\(11\) −3.81783 + 3.81783i −1.15112 + 1.15112i −0.164792 + 0.986328i \(0.552695\pi\)
−0.986328 + 0.164792i \(0.947305\pi\)
\(12\) 0 0
\(13\) 0.772847 0.772847i 0.214349 0.214349i −0.591763 0.806112i \(-0.701568\pi\)
0.806112 + 0.591763i \(0.201568\pi\)
\(14\) 2.80143 3.09023i 0.748714 0.825898i
\(15\) 0 0
\(16\) −3.92348 + 0.778653i −0.980870 + 0.194663i
\(17\) 2.27916 0.552778 0.276389 0.961046i \(-0.410862\pi\)
0.276389 + 0.961046i \(0.410862\pi\)
\(18\) 0 0
\(19\) −5.18129 + 5.18129i −1.18867 + 1.18867i −0.211233 + 0.977436i \(0.567748\pi\)
−0.977436 + 0.211233i \(0.932252\pi\)
\(20\) 4.44329 + 0.507134i 0.993550 + 0.113399i
\(21\) 0 0
\(22\) 7.62651 0.373835i 1.62598 0.0797018i
\(23\) −2.63370 −0.549164 −0.274582 0.961564i \(-0.588539\pi\)
−0.274582 + 0.961564i \(0.588539\pi\)
\(24\) 0 0
\(25\) −4.55890 2.05340i −0.911779 0.410681i
\(26\) −1.54384 + 0.0756756i −0.302772 + 0.0148412i
\(27\) 0 0
\(28\) −5.87045 + 0.576899i −1.10941 + 0.109024i
\(29\) −3.25626 + 3.25626i −0.604673 + 0.604673i −0.941549 0.336876i \(-0.890630\pi\)
0.336876 + 0.941549i \(0.390630\pi\)
\(30\) 0 0
\(31\) 1.93666i 0.347835i −0.984760 0.173917i \(-0.944357\pi\)
0.984760 0.173917i \(-0.0556426\pi\)
\(32\) 4.85046 + 2.91084i 0.857449 + 0.514569i
\(33\) 0 0
\(34\) −2.38802 2.16484i −0.409541 0.371268i
\(35\) 6.44789 + 1.38511i 1.08989 + 0.234126i
\(36\) 0 0
\(37\) 2.66367 + 2.66367i 0.437904 + 0.437904i 0.891306 0.453402i \(-0.149790\pi\)
−0.453402 + 0.891306i \(0.649790\pi\)
\(38\) 10.3501 0.507341i 1.67902 0.0823016i
\(39\) 0 0
\(40\) −4.17380 4.75178i −0.659936 0.751322i
\(41\) 1.01630 0.158719 0.0793596 0.996846i \(-0.474712\pi\)
0.0793596 + 0.996846i \(0.474712\pi\)
\(42\) 0 0
\(43\) −4.46535 + 4.46535i −0.680959 + 0.680959i −0.960216 0.279257i \(-0.909912\pi\)
0.279257 + 0.960216i \(0.409912\pi\)
\(44\) −8.34584 6.85229i −1.25818 1.03302i
\(45\) 0 0
\(46\) 2.75948 + 2.50160i 0.406864 + 0.368840i
\(47\) 6.93871i 1.01211i −0.862500 0.506057i \(-0.831102\pi\)
0.862500 0.506057i \(-0.168898\pi\)
\(48\) 0 0
\(49\) −1.69876 −0.242680
\(50\) 2.82622 + 6.48170i 0.399688 + 0.916651i
\(51\) 0 0
\(52\) 1.68945 + 1.38711i 0.234285 + 0.192358i
\(53\) −9.01752 + 9.01752i −1.23865 + 1.23865i −0.278099 + 0.960552i \(0.589704\pi\)
−0.960552 + 0.278099i \(0.910296\pi\)
\(54\) 0 0
\(55\) 6.55356 + 10.1395i 0.883682 + 1.36721i
\(56\) 6.69879 + 4.97155i 0.895163 + 0.664351i
\(57\) 0 0
\(58\) 6.50472 0.318847i 0.854111 0.0418666i
\(59\) −2.82309 + 2.82309i −0.367536 + 0.367536i −0.866578 0.499042i \(-0.833685\pi\)
0.499042 + 0.866578i \(0.333685\pi\)
\(60\) 0 0
\(61\) 10.8603 + 10.8603i 1.39052 + 1.39052i 0.824154 + 0.566365i \(0.191651\pi\)
0.566365 + 0.824154i \(0.308349\pi\)
\(62\) −1.83952 + 2.02916i −0.233620 + 0.257703i
\(63\) 0 0
\(64\) −2.31728 7.65704i −0.289660 0.957130i
\(65\) −1.32664 2.05255i −0.164550 0.254587i
\(66\) 0 0
\(67\) 7.21414 + 7.21414i 0.881347 + 0.881347i 0.993672 0.112324i \(-0.0358296\pi\)
−0.112324 + 0.993672i \(0.535830\pi\)
\(68\) 0.445807 + 4.53647i 0.0540620 + 0.550128i
\(69\) 0 0
\(70\) −5.44020 7.57574i −0.650229 0.905474i
\(71\) 8.03085i 0.953087i 0.879151 + 0.476543i \(0.158110\pi\)
−0.879151 + 0.476543i \(0.841890\pi\)
\(72\) 0 0
\(73\) 1.58003 0.184929 0.0924645 0.995716i \(-0.470526\pi\)
0.0924645 + 0.995716i \(0.470526\pi\)
\(74\) −0.260821 5.32095i −0.0303198 0.618548i
\(75\) 0 0
\(76\) −11.3264 9.29943i −1.29922 1.06672i
\(77\) −11.2602 11.2602i −1.28322 1.28322i
\(78\) 0 0
\(79\) 0.288222i 0.0324275i 0.999869 + 0.0162137i \(0.00516122\pi\)
−0.999869 + 0.0162137i \(0.994839\pi\)
\(80\) −0.140294 + 8.94317i −0.0156853 + 0.999877i
\(81\) 0 0
\(82\) −1.06484 0.965323i −0.117592 0.106602i
\(83\) 8.90062 8.90062i 0.976970 0.976970i −0.0227710 0.999741i \(-0.507249\pi\)
0.999741 + 0.0227710i \(0.00724886\pi\)
\(84\) 0 0
\(85\) 1.07036 4.98270i 0.116097 0.540449i
\(86\) 8.91999 0.437238i 0.961867 0.0471486i
\(87\) 0 0
\(88\) 2.23584 + 15.1068i 0.238341 + 1.61039i
\(89\) −6.44258 −0.682912 −0.341456 0.939898i \(-0.610920\pi\)
−0.341456 + 0.939898i \(0.610920\pi\)
\(90\) 0 0
\(91\) 2.27941 + 2.27941i 0.238947 + 0.238947i
\(92\) −0.515154 5.24214i −0.0537085 0.546531i
\(93\) 0 0
\(94\) −6.59067 + 7.27010i −0.679776 + 0.749853i
\(95\) 8.89402 + 13.7606i 0.912507 + 1.41181i
\(96\) 0 0
\(97\) 18.1267i 1.84049i −0.391342 0.920245i \(-0.627989\pi\)
0.391342 0.920245i \(-0.372011\pi\)
\(98\) 1.77989 + 1.61355i 0.179796 + 0.162994i
\(99\) 0 0
\(100\) 3.19539 9.47573i 0.319539 0.947573i
\(101\) 11.2655 + 11.2655i 1.12096 + 1.12096i 0.991598 + 0.129357i \(0.0412913\pi\)
0.129357 + 0.991598i \(0.458709\pi\)
\(102\) 0 0
\(103\) 4.58275i 0.451552i −0.974179 0.225776i \(-0.927508\pi\)
0.974179 0.225776i \(-0.0724918\pi\)
\(104\) −0.452603 3.05808i −0.0443813 0.299869i
\(105\) 0 0
\(106\) 18.0134 0.882977i 1.74962 0.0857623i
\(107\) 2.70168 + 2.70168i 0.261181 + 0.261181i 0.825534 0.564353i \(-0.190874\pi\)
−0.564353 + 0.825534i \(0.690874\pi\)
\(108\) 0 0
\(109\) 5.05700 + 5.05700i 0.484372 + 0.484372i 0.906525 0.422152i \(-0.138725\pi\)
−0.422152 + 0.906525i \(0.638725\pi\)
\(110\) 2.76436 16.8486i 0.263571 1.60645i
\(111\) 0 0
\(112\) −2.29653 11.5718i −0.217002 1.09343i
\(113\) −11.0909 −1.04334 −0.521672 0.853146i \(-0.674691\pi\)
−0.521672 + 0.853146i \(0.674691\pi\)
\(114\) 0 0
\(115\) −1.23686 + 5.75778i −0.115338 + 0.536915i
\(116\) −7.11824 5.84438i −0.660912 0.542637i
\(117\) 0 0
\(118\) 5.63942 0.276432i 0.519150 0.0254476i
\(119\) 6.72209i 0.616213i
\(120\) 0 0
\(121\) 18.1517i 1.65016i
\(122\) −1.06342 21.6946i −0.0962774 1.96413i
\(123\) 0 0
\(124\) 3.85475 0.378813i 0.346167 0.0340184i
\(125\) −6.63013 + 9.00230i −0.593017 + 0.805190i
\(126\) 0 0
\(127\) 10.4288 0.925403 0.462701 0.886514i \(-0.346880\pi\)
0.462701 + 0.886514i \(0.346880\pi\)
\(128\) −4.84502 + 10.2238i −0.428244 + 0.903663i
\(129\) 0 0
\(130\) −0.559591 + 3.41068i −0.0490794 + 0.299136i
\(131\) −13.5532 13.5532i −1.18415 1.18415i −0.978659 0.205491i \(-0.934121\pi\)
−0.205491 0.978659i \(-0.565879\pi\)
\(132\) 0 0
\(133\) −15.2815 15.2815i −1.32507 1.32507i
\(134\) −0.706394 14.4110i −0.0610231 1.24492i
\(135\) 0 0
\(136\) 3.84183 5.17658i 0.329435 0.443888i
\(137\) 7.61130i 0.650278i 0.945666 + 0.325139i \(0.105411\pi\)
−0.945666 + 0.325139i \(0.894589\pi\)
\(138\) 0 0
\(139\) 1.68008 + 1.68008i 0.142502 + 0.142502i 0.774759 0.632257i \(-0.217871\pi\)
−0.632257 + 0.774759i \(0.717871\pi\)
\(140\) −1.49572 + 13.1049i −0.126412 + 1.10756i
\(141\) 0 0
\(142\) 7.62804 8.41440i 0.640131 0.706121i
\(143\) 5.90120i 0.493484i
\(144\) 0 0
\(145\) 5.58959 + 8.64807i 0.464190 + 0.718183i
\(146\) −1.65550 1.50078i −0.137010 0.124206i
\(147\) 0 0
\(148\) −4.78078 + 5.82281i −0.392978 + 0.478632i
\(149\) −13.1900 13.1900i −1.08057 1.08057i −0.996456 0.0841097i \(-0.973195\pi\)
−0.0841097 0.996456i \(-0.526805\pi\)
\(150\) 0 0
\(151\) −14.8005 −1.20444 −0.602222 0.798329i \(-0.705718\pi\)
−0.602222 + 0.798329i \(0.705718\pi\)
\(152\) 3.03432 + 20.5018i 0.246116 + 1.66292i
\(153\) 0 0
\(154\) 1.10257 + 22.4934i 0.0888480 + 1.81257i
\(155\) −4.23392 0.909513i −0.340077 0.0730539i
\(156\) 0 0
\(157\) −10.2112 + 10.2112i −0.814942 + 0.814942i −0.985370 0.170428i \(-0.945485\pi\)
0.170428 + 0.985370i \(0.445485\pi\)
\(158\) 0.273765 0.301987i 0.0217796 0.0240248i
\(159\) 0 0
\(160\) 8.64159 9.23704i 0.683178 0.730252i
\(161\) 7.76774i 0.612184i
\(162\) 0 0
\(163\) −11.3893 11.3893i −0.892077 0.892077i 0.102641 0.994718i \(-0.467271\pi\)
−0.994718 + 0.102641i \(0.967271\pi\)
\(164\) 0.198789 + 2.02285i 0.0155228 + 0.157958i
\(165\) 0 0
\(166\) −17.7799 + 0.871530i −1.37999 + 0.0676439i
\(167\) 10.0783 0.779880 0.389940 0.920840i \(-0.372496\pi\)
0.389940 + 0.920840i \(0.372496\pi\)
\(168\) 0 0
\(169\) 11.8054i 0.908109i
\(170\) −5.85425 + 4.20399i −0.449001 + 0.322432i
\(171\) 0 0
\(172\) −9.76131 8.01446i −0.744293 0.611097i
\(173\) −9.02442 9.02442i −0.686114 0.686114i 0.275257 0.961371i \(-0.411237\pi\)
−0.961371 + 0.275257i \(0.911237\pi\)
\(174\) 0 0
\(175\) 6.05624 13.4459i 0.457809 1.01641i
\(176\) 12.0064 17.9520i 0.905019 1.35318i
\(177\) 0 0
\(178\) 6.75028 + 6.11943i 0.505955 + 0.458671i
\(179\) −10.3226 10.3226i −0.771547 0.771547i 0.206830 0.978377i \(-0.433685\pi\)
−0.978377 + 0.206830i \(0.933685\pi\)
\(180\) 0 0
\(181\) 13.9184 13.9184i 1.03455 1.03455i 0.0351674 0.999381i \(-0.488804\pi\)
0.999381 0.0351674i \(-0.0111964\pi\)
\(182\) −0.223195 4.55335i −0.0165443 0.337517i
\(183\) 0 0
\(184\) −4.43945 + 5.98182i −0.327281 + 0.440986i
\(185\) 7.07423 4.57236i 0.520108 0.336167i
\(186\) 0 0
\(187\) −8.70147 + 8.70147i −0.636314 + 0.636314i
\(188\) 13.8109 1.35722i 1.00726 0.0989853i
\(189\) 0 0
\(190\) 3.75159 22.8657i 0.272169 1.65885i
\(191\) 12.3885 0.896403 0.448202 0.893932i \(-0.352065\pi\)
0.448202 + 0.893932i \(0.352065\pi\)
\(192\) 0 0
\(193\) 23.2784i 1.67562i −0.545965 0.837808i \(-0.683837\pi\)
0.545965 0.837808i \(-0.316163\pi\)
\(194\) −17.2175 + 18.9925i −1.23615 + 1.36358i
\(195\) 0 0
\(196\) −0.332279 3.38123i −0.0237342 0.241517i
\(197\) 0.494769 0.494769i 0.0352508 0.0352508i −0.689262 0.724513i \(-0.742065\pi\)
0.724513 + 0.689262i \(0.242065\pi\)
\(198\) 0 0
\(199\) 2.97860 0.211147 0.105574 0.994411i \(-0.466332\pi\)
0.105574 + 0.994411i \(0.466332\pi\)
\(200\) −12.3484 + 6.89317i −0.873167 + 0.487421i
\(201\) 0 0
\(202\) −1.10309 22.5039i −0.0776132 1.58337i
\(203\) −9.60392 9.60392i −0.674063 0.674063i
\(204\) 0 0
\(205\) 0.477284 2.22183i 0.0333349 0.155179i
\(206\) −4.35289 + 4.80163i −0.303280 + 0.334545i
\(207\) 0 0
\(208\) −2.43047 + 3.63403i −0.168523 + 0.251975i
\(209\) 39.5626i 2.73660i
\(210\) 0 0
\(211\) −9.97252 + 9.97252i −0.686537 + 0.686537i −0.961465 0.274928i \(-0.911346\pi\)
0.274928 + 0.961465i \(0.411346\pi\)
\(212\) −19.7124 16.1847i −1.35385 1.11157i
\(213\) 0 0
\(214\) −0.264543 5.39688i −0.0180838 0.368923i
\(215\) 7.66506 + 11.8592i 0.522753 + 0.808790i
\(216\) 0 0
\(217\) 5.71192 0.387751
\(218\) −0.495171 10.1019i −0.0335372 0.684185i
\(219\) 0 0
\(220\) −18.8999 + 15.0276i −1.27423 + 1.01316i
\(221\) 1.76144 1.76144i 0.118488 0.118488i
\(222\) 0 0
\(223\) 1.35577 0.0907889 0.0453945 0.998969i \(-0.485546\pi\)
0.0453945 + 0.998969i \(0.485546\pi\)
\(224\) −8.58514 + 14.3058i −0.573619 + 0.955846i
\(225\) 0 0
\(226\) 11.6206 + 10.5346i 0.772990 + 0.700751i
\(227\) −0.282506 + 0.282506i −0.0187506 + 0.0187506i −0.716420 0.697669i \(-0.754220\pi\)
0.697669 + 0.716420i \(0.254220\pi\)
\(228\) 0 0
\(229\) 3.61973 3.61973i 0.239199 0.239199i −0.577320 0.816518i \(-0.695901\pi\)
0.816518 + 0.577320i \(0.195901\pi\)
\(230\) 6.76491 4.85794i 0.446065 0.320323i
\(231\) 0 0
\(232\) 1.90697 + 12.8847i 0.125198 + 0.845922i
\(233\) 19.3142i 1.26531i 0.774432 + 0.632657i \(0.218036\pi\)
−0.774432 + 0.632657i \(0.781964\pi\)
\(234\) 0 0
\(235\) −15.1694 3.25862i −0.989540 0.212569i
\(236\) −6.17132 5.06692i −0.401719 0.329828i
\(237\) 0 0
\(238\) 6.38492 7.04313i 0.413873 0.456538i
\(239\) 12.7616 0.825481 0.412740 0.910849i \(-0.364572\pi\)
0.412740 + 0.910849i \(0.364572\pi\)
\(240\) 0 0
\(241\) −9.03963 −0.582294 −0.291147 0.956678i \(-0.594037\pi\)
−0.291147 + 0.956678i \(0.594037\pi\)
\(242\) −17.2413 + 19.0186i −1.10831 + 1.22256i
\(243\) 0 0
\(244\) −19.4922 + 23.7408i −1.24786 + 1.51985i
\(245\) −0.797788 + 3.71382i −0.0509688 + 0.237267i
\(246\) 0 0
\(247\) 8.00868i 0.509580i
\(248\) −4.39867 3.26450i −0.279316 0.207296i
\(249\) 0 0
\(250\) 15.4975 3.13467i 0.980151 0.198254i
\(251\) 7.63101 7.63101i 0.481665 0.481665i −0.423998 0.905663i \(-0.639374\pi\)
0.905663 + 0.423998i \(0.139374\pi\)
\(252\) 0 0
\(253\) 10.0550 10.0550i 0.632154 0.632154i
\(254\) −10.9268 9.90567i −0.685611 0.621537i
\(255\) 0 0
\(256\) 14.7874 6.11006i 0.924212 0.381879i
\(257\) 9.14111 0.570207 0.285103 0.958497i \(-0.407972\pi\)
0.285103 + 0.958497i \(0.407972\pi\)
\(258\) 0 0
\(259\) −7.85613 + 7.85613i −0.488156 + 0.488156i
\(260\) 3.82592 3.04205i 0.237274 0.188660i
\(261\) 0 0
\(262\) 1.32710 + 27.0739i 0.0819887 + 1.67263i
\(263\) −5.35127 −0.329974 −0.164987 0.986296i \(-0.552758\pi\)
−0.164987 + 0.986296i \(0.552758\pi\)
\(264\) 0 0
\(265\) 15.4792 + 23.9489i 0.950877 + 1.47117i
\(266\) 1.49633 + 30.5264i 0.0917461 + 1.87169i
\(267\) 0 0
\(268\) −12.9480 + 15.7702i −0.790926 + 0.963318i
\(269\) −17.5132 + 17.5132i −1.06780 + 1.06780i −0.0702731 + 0.997528i \(0.522387\pi\)
−0.997528 + 0.0702731i \(0.977613\pi\)
\(270\) 0 0
\(271\) 14.8401i 0.901471i 0.892657 + 0.450736i \(0.148838\pi\)
−0.892657 + 0.450736i \(0.851162\pi\)
\(272\) −8.94225 + 1.77468i −0.542204 + 0.107606i
\(273\) 0 0
\(274\) 7.22953 7.97482i 0.436752 0.481776i
\(275\) 25.2447 9.56556i 1.52231 0.576825i
\(276\) 0 0
\(277\) 9.59587 + 9.59587i 0.576560 + 0.576560i 0.933954 0.357394i \(-0.116335\pi\)
−0.357394 + 0.933954i \(0.616335\pi\)
\(278\) −0.164510 3.35613i −0.00986665 0.201287i
\(279\) 0 0
\(280\) 14.0147 12.3101i 0.837540 0.735667i
\(281\) 24.1743 1.44212 0.721059 0.692874i \(-0.243656\pi\)
0.721059 + 0.692874i \(0.243656\pi\)
\(282\) 0 0
\(283\) 22.5338 22.5338i 1.33950 1.33950i 0.442950 0.896546i \(-0.353932\pi\)
0.896546 0.442950i \(-0.146068\pi\)
\(284\) −15.9847 + 1.57084i −0.948518 + 0.0932124i
\(285\) 0 0
\(286\) 5.60521 6.18304i 0.331443 0.365611i
\(287\) 2.99744i 0.176933i
\(288\) 0 0
\(289\) −11.8054 −0.694436
\(290\) 2.35775 14.3703i 0.138452 0.843854i
\(291\) 0 0
\(292\) 0.309057 + 3.14492i 0.0180862 + 0.184043i
\(293\) −2.21485 + 2.21485i −0.129393 + 0.129393i −0.768837 0.639445i \(-0.779164\pi\)
0.639445 + 0.768837i \(0.279164\pi\)
\(294\) 0 0
\(295\) 4.84603 + 7.49764i 0.282147 + 0.436530i
\(296\) 10.5399 1.55992i 0.612617 0.0906687i
\(297\) 0 0
\(298\) 1.29154 + 26.3483i 0.0748167 + 1.52632i
\(299\) −2.03545 + 2.03545i −0.117713 + 0.117713i
\(300\) 0 0
\(301\) −13.1699 13.1699i −0.759103 0.759103i
\(302\) 15.5073 + 14.0581i 0.892346 + 0.808952i
\(303\) 0 0
\(304\) 16.2942 24.3631i 0.934539 1.39732i
\(305\) 28.8431 18.6424i 1.65155 1.06746i
\(306\) 0 0
\(307\) −12.5025 12.5025i −0.713556 0.713556i 0.253722 0.967277i \(-0.418345\pi\)
−0.967277 + 0.253722i \(0.918345\pi\)
\(308\) 20.2099 24.6149i 1.15157 1.40257i
\(309\) 0 0
\(310\) 3.57224 + 4.97450i 0.202889 + 0.282533i
\(311\) 3.75997i 0.213209i 0.994302 + 0.106604i \(0.0339978\pi\)
−0.994302 + 0.106604i \(0.966002\pi\)
\(312\) 0 0
\(313\) −6.19979 −0.350433 −0.175216 0.984530i \(-0.556062\pi\)
−0.175216 + 0.984530i \(0.556062\pi\)
\(314\) 20.3979 0.999859i 1.15112 0.0564253i
\(315\) 0 0
\(316\) −0.573680 + 0.0563765i −0.0322720 + 0.00317143i
\(317\) 13.6244 + 13.6244i 0.765221 + 0.765221i 0.977261 0.212040i \(-0.0680108\pi\)
−0.212040 + 0.977261i \(0.568011\pi\)
\(318\) 0 0
\(319\) 24.8638i 1.39210i
\(320\) −17.8280 + 1.47005i −0.996618 + 0.0821784i
\(321\) 0 0
\(322\) −7.37812 + 8.13873i −0.411167 + 0.453553i
\(323\) −11.8090 + 11.8090i −0.657070 + 0.657070i
\(324\) 0 0
\(325\) −5.11030 + 1.93636i −0.283468 + 0.107410i
\(326\) 1.11521 + 22.7512i 0.0617660 + 1.26007i
\(327\) 0 0
\(328\) 1.71311 2.30828i 0.0945905 0.127454i
\(329\) 20.4648 1.12826
\(330\) 0 0
\(331\) 11.4420 + 11.4420i 0.628910 + 0.628910i 0.947794 0.318884i \(-0.103308\pi\)
−0.318884 + 0.947794i \(0.603308\pi\)
\(332\) 19.4569 + 15.9749i 1.06783 + 0.876738i
\(333\) 0 0
\(334\) −10.5596 9.57276i −0.577796 0.523798i
\(335\) 19.1595 12.3835i 1.04679 0.676585i
\(336\) 0 0
\(337\) 9.70392i 0.528606i −0.964440 0.264303i \(-0.914858\pi\)
0.964440 0.264303i \(-0.0851419\pi\)
\(338\) 11.2133 12.3692i 0.609922 0.672798i
\(339\) 0 0
\(340\) 10.1270 + 1.15584i 0.549213 + 0.0626843i
\(341\) 7.39385 + 7.39385i 0.400400 + 0.400400i
\(342\) 0 0
\(343\) 15.6353i 0.844227i
\(344\) 2.61504 + 17.6689i 0.140994 + 0.952645i
\(345\) 0 0
\(346\) 0.883653 + 18.0272i 0.0475055 + 0.969149i
\(347\) 16.6678 + 16.6678i 0.894776 + 0.894776i 0.994968 0.100192i \(-0.0319458\pi\)
−0.100192 + 0.994968i \(0.531946\pi\)
\(348\) 0 0
\(349\) 0.985320 + 0.985320i 0.0527430 + 0.0527430i 0.732986 0.680243i \(-0.238126\pi\)
−0.680243 + 0.732986i \(0.738126\pi\)
\(350\) −19.1169 + 8.33556i −1.02184 + 0.445554i
\(351\) 0 0
\(352\) −29.6314 + 7.40514i −1.57936 + 0.394695i
\(353\) 18.6331 0.991742 0.495871 0.868396i \(-0.334849\pi\)
0.495871 + 0.868396i \(0.334849\pi\)
\(354\) 0 0
\(355\) 17.5570 + 3.77152i 0.931829 + 0.200172i
\(356\) −1.26018 12.8234i −0.0667892 0.679638i
\(357\) 0 0
\(358\) 1.01077 + 20.6204i 0.0534207 + 1.08982i
\(359\) 15.6789i 0.827503i −0.910390 0.413751i \(-0.864218\pi\)
0.910390 0.413751i \(-0.135782\pi\)
\(360\) 0 0
\(361\) 34.6914i 1.82586i
\(362\) −27.8035 + 1.36286i −1.46132 + 0.0716306i
\(363\) 0 0
\(364\) −4.09111 + 4.98282i −0.214432 + 0.261171i
\(365\) 0.742031 3.45426i 0.0388397 0.180804i
\(366\) 0 0
\(367\) 24.8012 1.29461 0.647305 0.762231i \(-0.275896\pi\)
0.647305 + 0.762231i \(0.275896\pi\)
\(368\) 10.3333 2.05074i 0.538659 0.106902i
\(369\) 0 0
\(370\) −11.7551 1.92867i −0.611119 0.100267i
\(371\) −26.5960 26.5960i −1.38079 1.38079i
\(372\) 0 0
\(373\) 7.99818 + 7.99818i 0.414130 + 0.414130i 0.883175 0.469045i \(-0.155402\pi\)
−0.469045 + 0.883175i \(0.655402\pi\)
\(374\) 17.3821 0.852030i 0.898805 0.0440574i
\(375\) 0 0
\(376\) −15.7596 11.6961i −0.812741 0.603181i
\(377\) 5.03319i 0.259222i
\(378\) 0 0
\(379\) −5.54375 5.54375i −0.284763 0.284763i 0.550242 0.835005i \(-0.314536\pi\)
−0.835005 + 0.550242i \(0.814536\pi\)
\(380\) −25.6496 + 20.3943i −1.31579 + 1.04621i
\(381\) 0 0
\(382\) −12.9802 11.7672i −0.664126 0.602060i
\(383\) 35.2874i 1.80310i 0.432675 + 0.901550i \(0.357570\pi\)
−0.432675 + 0.901550i \(0.642430\pi\)
\(384\) 0 0
\(385\) −29.9051 + 19.3289i −1.52410 + 0.985090i
\(386\) −22.1108 + 24.3902i −1.12541 + 1.24143i
\(387\) 0 0
\(388\) 36.0797 3.54561i 1.83167 0.180001i
\(389\) 10.5078 + 10.5078i 0.532767 + 0.532767i 0.921395 0.388628i \(-0.127051\pi\)
−0.388628 + 0.921395i \(0.627051\pi\)
\(390\) 0 0
\(391\) −6.00263 −0.303566
\(392\) −2.86349 + 3.85833i −0.144628 + 0.194875i
\(393\) 0 0
\(394\) −0.988352 + 0.0484468i −0.0497924 + 0.00244071i
\(395\) 0.630109 + 0.135357i 0.0317042 + 0.00681057i
\(396\) 0 0
\(397\) −10.4175 + 10.4175i −0.522838 + 0.522838i −0.918427 0.395589i \(-0.870540\pi\)
0.395589 + 0.918427i \(0.370540\pi\)
\(398\) −3.12086 2.82920i −0.156434 0.141815i
\(399\) 0 0
\(400\) 19.4856 + 4.50669i 0.974282 + 0.225334i
\(401\) 15.4212i 0.770099i 0.922896 + 0.385049i \(0.125816\pi\)
−0.922896 + 0.385049i \(0.874184\pi\)
\(402\) 0 0
\(403\) −1.49674 1.49674i −0.0745581 0.0745581i
\(404\) −20.2194 + 24.6264i −1.00595 + 1.22521i
\(405\) 0 0
\(406\) 0.940396 + 19.1848i 0.0466711 + 0.952125i
\(407\) −20.3389 −1.00816
\(408\) 0 0
\(409\) 5.10228i 0.252291i −0.992012 0.126146i \(-0.959739\pi\)
0.992012 0.126146i \(-0.0402607\pi\)
\(410\) −2.61046 + 1.87460i −0.128922 + 0.0925797i
\(411\) 0 0
\(412\) 9.12157 0.896392i 0.449388 0.0441621i
\(413\) −8.32634 8.32634i −0.409712 0.409712i
\(414\) 0 0
\(415\) −15.2785 23.6385i −0.749992 1.16037i
\(416\) 5.99830 1.49903i 0.294091 0.0734959i
\(417\) 0 0
\(418\) −37.5782 + 41.4521i −1.83801 + 2.02749i
\(419\) 0.0584508 + 0.0584508i 0.00285551 + 0.00285551i 0.708533 0.705678i \(-0.249357\pi\)
−0.705678 + 0.708533i \(0.749357\pi\)
\(420\) 0 0
\(421\) −6.66123 + 6.66123i −0.324648 + 0.324648i −0.850547 0.525899i \(-0.823729\pi\)
0.525899 + 0.850547i \(0.323729\pi\)
\(422\) 19.9211 0.976489i 0.969745 0.0475347i
\(423\) 0 0
\(424\) 5.28093 + 35.6814i 0.256465 + 1.73284i
\(425\) −10.3905 4.68004i −0.504012 0.227015i
\(426\) 0 0
\(427\) −32.0310 + 32.0310i −1.55009 + 1.55009i
\(428\) −4.84900 + 5.90590i −0.234385 + 0.285473i
\(429\) 0 0
\(430\) 3.23320 19.7062i 0.155919 0.950316i
\(431\) −12.3929 −0.596946 −0.298473 0.954418i \(-0.596477\pi\)
−0.298473 + 0.954418i \(0.596477\pi\)
\(432\) 0 0
\(433\) 6.31623i 0.303539i −0.988416 0.151769i \(-0.951503\pi\)
0.988416 0.151769i \(-0.0484971\pi\)
\(434\) −5.98472 5.42542i −0.287276 0.260429i
\(435\) 0 0
\(436\) −9.07635 + 11.0547i −0.434678 + 0.529422i
\(437\) 13.6459 13.6459i 0.652774 0.652774i
\(438\) 0 0
\(439\) −5.22876 −0.249555 −0.124778 0.992185i \(-0.539822\pi\)
−0.124778 + 0.992185i \(0.539822\pi\)
\(440\) 34.0764 + 2.20661i 1.62453 + 0.105196i
\(441\) 0 0
\(442\) −3.51867 + 0.172477i −0.167366 + 0.00820390i
\(443\) −4.30848 4.30848i −0.204702 0.204702i 0.597309 0.802011i \(-0.296237\pi\)
−0.802011 + 0.597309i \(0.796237\pi\)
\(444\) 0 0
\(445\) −3.02562 + 14.0847i −0.143428 + 0.667680i
\(446\) −1.42052 1.28776i −0.0672635 0.0609774i
\(447\) 0 0
\(448\) 22.5834 6.83450i 1.06697 0.322900i
\(449\) 22.8023i 1.07611i 0.842911 + 0.538053i \(0.180840\pi\)
−0.842911 + 0.538053i \(0.819160\pi\)
\(450\) 0 0
\(451\) −3.88006 + 3.88006i −0.182705 + 0.182705i
\(452\) −2.16939 22.0755i −0.102040 1.03834i
\(453\) 0 0
\(454\) 0.564334 0.0276624i 0.0264855 0.00129826i
\(455\) 6.05371 3.91276i 0.283802 0.183433i
\(456\) 0 0
\(457\) −23.8294 −1.11469 −0.557345 0.830281i \(-0.688180\pi\)
−0.557345 + 0.830281i \(0.688180\pi\)
\(458\) −7.23078 + 0.354437i −0.337872 + 0.0165617i
\(459\) 0 0
\(460\) −11.7023 1.33564i −0.545622 0.0622744i
\(461\) −7.75855 + 7.75855i −0.361352 + 0.361352i −0.864310 0.502959i \(-0.832245\pi\)
0.502959 + 0.864310i \(0.332245\pi\)
\(462\) 0 0
\(463\) −9.96705 −0.463208 −0.231604 0.972810i \(-0.574397\pi\)
−0.231604 + 0.972810i \(0.574397\pi\)
\(464\) 10.2404 15.3114i 0.475398 0.710813i
\(465\) 0 0
\(466\) 18.3454 20.2366i 0.849835 0.937443i
\(467\) 25.6782 25.6782i 1.18824 1.18824i 0.210692 0.977553i \(-0.432428\pi\)
0.977553 0.210692i \(-0.0675716\pi\)
\(468\) 0 0
\(469\) −21.2771 + 21.2771i −0.982487 + 0.982487i
\(470\) 12.7987 + 17.8227i 0.590359 + 0.822102i
\(471\) 0 0
\(472\) 1.65329 + 11.1707i 0.0760988 + 0.514173i
\(473\) 34.0959i 1.56773i
\(474\) 0 0
\(475\) 34.2602 12.9817i 1.57197 0.595640i
\(476\) −13.3797 + 1.31485i −0.613259 + 0.0602659i
\(477\) 0 0
\(478\) −13.3711 12.1215i −0.611581 0.554426i
\(479\) 19.8901 0.908803 0.454402 0.890797i \(-0.349853\pi\)
0.454402 + 0.890797i \(0.349853\pi\)
\(480\) 0 0
\(481\) 4.11722 0.187729
\(482\) 9.47137 + 8.58622i 0.431409 + 0.391092i
\(483\) 0 0
\(484\) 36.1294 3.55049i 1.64224 0.161386i
\(485\) −39.6286 8.51284i −1.79944 0.386548i
\(486\) 0 0
\(487\) 24.3871i 1.10508i −0.833485 0.552541i \(-0.813658\pi\)
0.833485 0.552541i \(-0.186342\pi\)
\(488\) 42.9731 6.36012i 1.94530 0.287909i
\(489\) 0 0
\(490\) 4.36343 3.13342i 0.197120 0.141554i
\(491\) −16.7013 + 16.7013i −0.753719 + 0.753719i −0.975171 0.221452i \(-0.928920\pi\)
0.221452 + 0.975171i \(0.428920\pi\)
\(492\) 0 0
\(493\) −7.42156 + 7.42156i −0.334250 + 0.334250i
\(494\) 7.60698 8.39118i 0.342254 0.377537i
\(495\) 0 0
\(496\) 1.50799 + 7.59845i 0.0677107 + 0.341181i
\(497\) −23.6859 −1.06246
\(498\) 0 0
\(499\) 6.16191 6.16191i 0.275845 0.275845i −0.555603 0.831448i \(-0.687512\pi\)
0.831448 + 0.555603i \(0.187512\pi\)
\(500\) −19.2151 11.4358i −0.859327 0.511426i
\(501\) 0 0
\(502\) −15.2437 + 0.747213i −0.680360 + 0.0333497i
\(503\) −15.6520 −0.697889 −0.348945 0.937143i \(-0.613460\pi\)
−0.348945 + 0.937143i \(0.613460\pi\)
\(504\) 0 0
\(505\) 29.9191 19.3379i 1.33138 0.860525i
\(506\) −20.0859 + 0.984567i −0.892928 + 0.0437693i
\(507\) 0 0
\(508\) 2.03988 + 20.7575i 0.0905049 + 0.920966i
\(509\) 13.0382 13.0382i 0.577908 0.577908i −0.356418 0.934326i \(-0.616002\pi\)
0.934326 + 0.356418i \(0.116002\pi\)
\(510\) 0 0
\(511\) 4.66010i 0.206151i
\(512\) −21.2972 7.64381i −0.941214 0.337812i
\(513\) 0 0
\(514\) −9.57769 8.68261i −0.422454 0.382973i
\(515\) −10.0188 2.15220i −0.441481 0.0948371i
\(516\) 0 0
\(517\) 26.4908 + 26.4908i 1.16507 + 1.16507i
\(518\) 15.6934 0.769256i 0.689529 0.0337992i
\(519\) 0 0
\(520\) −6.89811 0.446686i −0.302502 0.0195885i
\(521\) 11.6740 0.511445 0.255723 0.966750i \(-0.417687\pi\)
0.255723 + 0.966750i \(0.417687\pi\)
\(522\) 0 0
\(523\) 12.7738 12.7738i 0.558559 0.558559i −0.370338 0.928897i \(-0.620758\pi\)
0.928897 + 0.370338i \(0.120758\pi\)
\(524\) 24.3255 29.6275i 1.06266 1.29428i
\(525\) 0 0
\(526\) 5.60685 + 5.08286i 0.244470 + 0.221623i
\(527\) 4.41397i 0.192275i
\(528\) 0 0
\(529\) −16.0636 −0.698419
\(530\) 6.52927 39.7955i 0.283613 1.72861i
\(531\) 0 0
\(532\) 27.4274 33.4056i 1.18913 1.44832i
\(533\) 0.785444 0.785444i 0.0340213 0.0340213i
\(534\) 0 0
\(535\) 7.17518 4.63761i 0.310210 0.200501i
\(536\) 28.5456 4.22482i 1.23298 0.182484i
\(537\) 0 0
\(538\) 34.9845 1.71486i 1.50829 0.0739329i
\(539\) 6.48559 6.48559i 0.279354 0.279354i
\(540\) 0 0
\(541\) 23.1601 + 23.1601i 0.995729 + 0.995729i 0.999991 0.00426226i \(-0.00135673\pi\)
−0.00426226 + 0.999991i \(0.501357\pi\)
\(542\) 14.0957 15.5488i 0.605464 0.667880i
\(543\) 0 0
\(544\) 11.0550 + 6.63429i 0.473979 + 0.284443i
\(545\) 13.4305 8.68066i 0.575299 0.371839i
\(546\) 0 0
\(547\) −32.6697 32.6697i −1.39686 1.39686i −0.808873 0.587983i \(-0.799922\pi\)
−0.587983 0.808873i \(-0.700078\pi\)
\(548\) −15.1496 + 1.48878i −0.647160 + 0.0635975i
\(549\) 0 0
\(550\) −35.5361 13.9560i −1.51526 0.595087i
\(551\) 33.7433i 1.43751i
\(552\) 0 0
\(553\) −0.850072 −0.0361487
\(554\) −0.939608 19.1687i −0.0399201 0.814401i
\(555\) 0 0
\(556\) −3.01542 + 3.67267i −0.127882 + 0.155756i
\(557\) 27.6869 + 27.6869i 1.17313 + 1.17313i 0.981459 + 0.191673i \(0.0613912\pi\)
0.191673 + 0.981459i \(0.438609\pi\)
\(558\) 0 0
\(559\) 6.90206i 0.291926i
\(560\) −26.3767 0.413778i −1.11462 0.0174853i
\(561\) 0 0
\(562\) −25.3289 22.9618i −1.06843 0.968583i
\(563\) −12.9042 + 12.9042i −0.543845 + 0.543845i −0.924654 0.380809i \(-0.875646\pi\)
0.380809 + 0.924654i \(0.375646\pi\)
\(564\) 0 0
\(565\) −5.20861 + 24.2469i −0.219128 + 1.02007i
\(566\) −45.0136 + 2.20647i −1.89206 + 0.0927446i
\(567\) 0 0
\(568\) 18.2402 + 13.5371i 0.765341 + 0.568003i
\(569\) −39.4363 −1.65326 −0.826628 0.562749i \(-0.809744\pi\)
−0.826628 + 0.562749i \(0.809744\pi\)
\(570\) 0 0
\(571\) −1.54757 1.54757i −0.0647637 0.0647637i 0.673983 0.738747i \(-0.264582\pi\)
−0.738747 + 0.673983i \(0.764582\pi\)
\(572\) −11.7458 + 1.15428i −0.491118 + 0.0482630i
\(573\) 0 0
\(574\) 2.84709 3.14059i 0.118835 0.131086i
\(575\) 12.0068 + 5.40804i 0.500716 + 0.225531i
\(576\) 0 0
\(577\) 26.5133i 1.10376i 0.833923 + 0.551881i \(0.186090\pi\)
−0.833923 + 0.551881i \(0.813910\pi\)
\(578\) 12.3692 + 11.2133i 0.514492 + 0.466411i
\(579\) 0 0
\(580\) −16.1199 + 12.8172i −0.669342 + 0.532204i
\(581\) 26.2512 + 26.2512i 1.08908 + 1.08908i
\(582\) 0 0
\(583\) 68.8548i 2.85167i
\(584\) 2.66336 3.58868i 0.110211 0.148500i
\(585\) 0 0
\(586\) 4.42438 0.216873i 0.182769 0.00895895i
\(587\) 4.43417 + 4.43417i 0.183018 + 0.183018i 0.792669 0.609652i \(-0.208691\pi\)
−0.609652 + 0.792669i \(0.708691\pi\)
\(588\) 0 0
\(589\) 10.0344 + 10.0344i 0.413460 + 0.413460i
\(590\) 2.04410 12.4587i 0.0841544 0.512916i
\(591\) 0 0
\(592\) −12.5249 8.37677i −0.514771 0.344283i
\(593\) 20.0418 0.823019 0.411510 0.911405i \(-0.365002\pi\)
0.411510 + 0.911405i \(0.365002\pi\)
\(594\) 0 0
\(595\) 14.6958 + 3.15689i 0.602469 + 0.129420i
\(596\) 23.6735 28.8335i 0.969706 1.18107i
\(597\) 0 0
\(598\) 4.06601 0.199307i 0.166272 0.00815026i
\(599\) 30.5731i 1.24918i 0.780951 + 0.624592i \(0.214735\pi\)
−0.780951 + 0.624592i \(0.785265\pi\)
\(600\) 0 0
\(601\) 36.4715i 1.48770i 0.668344 + 0.743852i \(0.267003\pi\)
−0.668344 + 0.743852i \(0.732997\pi\)
\(602\) 1.28957 + 26.3083i 0.0525591 + 1.07225i
\(603\) 0 0
\(604\) −2.89498 29.4590i −0.117795 1.19867i
\(605\) −39.6832 8.52458i −1.61335 0.346573i
\(606\) 0 0
\(607\) 18.5659 0.753566 0.376783 0.926302i \(-0.377030\pi\)
0.376783 + 0.926302i \(0.377030\pi\)
\(608\) −40.2135 + 10.0497i −1.63087 + 0.407570i
\(609\) 0 0
\(610\) −47.9280 7.86357i −1.94055 0.318386i
\(611\) −5.36256 5.36256i −0.216946 0.216946i
\(612\) 0 0
\(613\) −17.3170 17.3170i −0.699425 0.699425i 0.264861 0.964286i \(-0.414674\pi\)
−0.964286 + 0.264861i \(0.914674\pi\)
\(614\) 1.22422 + 24.9750i 0.0494055 + 1.00791i
\(615\) 0 0
\(616\) −44.5554 + 6.59431i −1.79519 + 0.265692i
\(617\) 1.18526i 0.0477167i −0.999715 0.0238584i \(-0.992405\pi\)
0.999715 0.0238584i \(-0.00759508\pi\)
\(618\) 0 0
\(619\) −0.522478 0.522478i −0.0210002 0.0210002i 0.696529 0.717529i \(-0.254727\pi\)
−0.717529 + 0.696529i \(0.754727\pi\)
\(620\) 0.982147 8.60515i 0.0394440 0.345591i
\(621\) 0 0
\(622\) 3.57138 3.93955i 0.143199 0.157962i
\(623\) 19.0015i 0.761280i
\(624\) 0 0
\(625\) 16.5671 + 18.7225i 0.662683 + 0.748900i
\(626\) 6.49589 + 5.88882i 0.259628 + 0.235364i
\(627\) 0 0
\(628\) −22.3218 18.3272i −0.890737 0.731333i
\(629\) 6.07093 + 6.07093i 0.242064 + 0.242064i
\(630\) 0 0
\(631\) 33.4437 1.33137 0.665687 0.746231i \(-0.268139\pi\)
0.665687 + 0.746231i \(0.268139\pi\)
\(632\) 0.654628 + 0.485836i 0.0260397 + 0.0193255i
\(633\) 0 0
\(634\) −1.33407 27.2161i −0.0529827 1.08089i
\(635\) 4.89765 22.7993i 0.194357 0.904763i
\(636\) 0 0
\(637\) −1.31288 + 1.31288i −0.0520183 + 0.0520183i
\(638\) −23.6166 + 26.0512i −0.934991 + 1.03138i
\(639\) 0 0
\(640\) 20.0758 + 15.3936i 0.793566 + 0.608484i
\(641\) 0.0475126i 0.00187664i −1.00000 0.000938318i \(-0.999701\pi\)
1.00000 0.000938318i \(-0.000298676\pi\)
\(642\) 0 0
\(643\) −6.27347 6.27347i −0.247402 0.247402i 0.572502 0.819903i \(-0.305973\pi\)
−0.819903 + 0.572502i \(0.805973\pi\)
\(644\) 15.4610 1.51938i 0.609249 0.0598719i
\(645\) 0 0
\(646\) 23.5897 1.15631i 0.928123 0.0454945i
\(647\) −30.1491 −1.18529 −0.592643 0.805465i \(-0.701915\pi\)
−0.592643 + 0.805465i \(0.701915\pi\)
\(648\) 0 0
\(649\) 21.5562i 0.846155i
\(650\) 7.19360 + 2.82513i 0.282156 + 0.110811i
\(651\) 0 0
\(652\) 20.4416 24.8971i 0.800555 0.975046i
\(653\) −19.4196 19.4196i −0.759947 0.759947i 0.216365 0.976312i \(-0.430580\pi\)
−0.976312 + 0.216365i \(0.930580\pi\)
\(654\) 0 0
\(655\) −35.9950 + 23.2650i −1.40644 + 0.909038i
\(656\) −3.98743 + 0.791345i −0.155683 + 0.0308968i
\(657\) 0 0
\(658\) −21.4422 19.4383i −0.835903 0.757784i
\(659\) 29.1034 + 29.1034i 1.13371 + 1.13371i 0.989555 + 0.144153i \(0.0460457\pi\)
0.144153 + 0.989555i \(0.453954\pi\)
\(660\) 0 0
\(661\) 27.9971 27.9971i 1.08896 1.08896i 0.0933236 0.995636i \(-0.470251\pi\)
0.995636 0.0933236i \(-0.0297491\pi\)
\(662\) −1.12038 22.8566i −0.0435447 0.888346i
\(663\) 0 0
\(664\) −5.21247 35.2188i −0.202283 1.36676i
\(665\) −40.5850 + 26.2317i −1.57382 + 1.01722i
\(666\) 0 0
\(667\) 8.57602 8.57602i 0.332065 0.332065i
\(668\) 1.97132 + 20.0599i 0.0762727 + 0.776141i
\(669\) 0 0
\(670\) −31.8369 5.22350i −1.22997 0.201802i
\(671\) −82.9257 −3.20131
\(672\) 0 0
\(673\) 24.1910i 0.932495i 0.884654 + 0.466248i \(0.154394\pi\)
−0.884654 + 0.466248i \(0.845606\pi\)
\(674\) −9.21719 + 10.1674i −0.355033 + 0.391633i
\(675\) 0 0
\(676\) −23.4976 + 2.30915i −0.903755 + 0.0888135i
\(677\) 22.7749 22.7749i 0.875311 0.875311i −0.117734 0.993045i \(-0.537563\pi\)
0.993045 + 0.117734i \(0.0375631\pi\)
\(678\) 0 0
\(679\) 53.4624 2.05170
\(680\) −9.51278 10.8301i −0.364798 0.415314i
\(681\) 0 0
\(682\) −0.723991 14.7700i −0.0277230 0.565571i
\(683\) −11.1813 11.1813i −0.427842 0.427842i 0.460051 0.887893i \(-0.347831\pi\)
−0.887893 + 0.460051i \(0.847831\pi\)
\(684\) 0 0
\(685\) 16.6398 + 3.57449i 0.635774 + 0.136574i
\(686\) 14.8511 16.3820i 0.567016 0.625469i
\(687\) 0 0
\(688\) 14.0427 20.9967i 0.535375 0.800490i
\(689\) 13.9383i 0.531008i
\(690\) 0 0
\(691\) −30.4888 + 30.4888i −1.15985 + 1.15985i −0.175343 + 0.984507i \(0.556103\pi\)
−0.984507 + 0.175343i \(0.943897\pi\)
\(692\) 16.1971 19.7275i 0.615723 0.749927i
\(693\) 0 0
\(694\) −1.63208 33.2957i −0.0619529 1.26389i
\(695\) 4.46199 2.88397i 0.169253 0.109395i
\(696\) 0 0
\(697\) 2.31631 0.0877365
\(698\) −0.0964805 1.96828i −0.00365184 0.0745004i
\(699\) 0 0
\(700\) 27.9474 + 9.42438i 1.05631 + 0.356208i
\(701\) 10.1167 10.1167i 0.382102 0.382102i −0.489757 0.871859i \(-0.662914\pi\)
0.871859 + 0.489757i \(0.162914\pi\)
\(702\) 0 0
\(703\) −27.6024 −1.04105
\(704\) 38.0803 + 20.3863i 1.43520 + 0.768338i
\(705\) 0 0
\(706\) −19.5231 17.6985i −0.734760 0.666093i
\(707\) −33.2260 + 33.2260i −1.24959 + 1.24959i
\(708\) 0 0
\(709\) 10.9333 10.9333i 0.410608 0.410608i −0.471342 0.881950i \(-0.656230\pi\)
0.881950 + 0.471342i \(0.156230\pi\)
\(710\) −14.8132 20.6280i −0.555928 0.774156i
\(711\) 0 0
\(712\) −10.8598 + 14.6328i −0.406989 + 0.548387i
\(713\) 5.10058i 0.191018i
\(714\) 0 0
\(715\) 12.9012 + 2.77138i 0.482477 + 0.103644i
\(716\) 18.5271 22.5653i 0.692391 0.843306i
\(717\) 0 0
\(718\) −14.8925 + 16.4278i −0.555784 + 0.613079i
\(719\) 17.0081 0.634295 0.317148 0.948376i \(-0.397275\pi\)
0.317148 + 0.948376i \(0.397275\pi\)
\(720\) 0 0
\(721\) 13.5162 0.503370
\(722\) −32.9514 + 36.3483i −1.22632 + 1.35274i
\(723\) 0 0
\(724\) 30.4259 + 24.9810i 1.13077 + 0.928410i
\(725\) 21.5314 8.15855i 0.799656 0.303001i
\(726\) 0 0
\(727\) 9.36040i 0.347158i 0.984820 + 0.173579i \(0.0555332\pi\)
−0.984820 + 0.173579i \(0.944467\pi\)
\(728\) 9.01939 1.33489i 0.334281 0.0494743i
\(729\) 0 0
\(730\) −4.05847 + 2.91443i −0.150211 + 0.107868i
\(731\) −10.1773 + 10.1773i −0.376420 + 0.376420i
\(732\) 0 0
\(733\) −0.534164 + 0.534164i −0.0197298 + 0.0197298i −0.716903 0.697173i \(-0.754441\pi\)
0.697173 + 0.716903i \(0.254441\pi\)
\(734\) −25.9857 23.5572i −0.959148 0.869511i
\(735\) 0 0
\(736\) −12.7747 7.66628i −0.470880 0.282583i
\(737\) −55.0848 −2.02907
\(738\) 0 0
\(739\) 29.8329 29.8329i 1.09742 1.09742i 0.102708 0.994712i \(-0.467249\pi\)
0.994712 0.102708i \(-0.0327506\pi\)
\(740\) 10.4846 + 13.1863i 0.385422 + 0.484737i
\(741\) 0 0
\(742\) 2.60422 + 53.1281i 0.0956040 + 1.95040i
\(743\) −18.5297 −0.679788 −0.339894 0.940464i \(-0.610391\pi\)
−0.339894 + 0.940464i \(0.610391\pi\)
\(744\) 0 0
\(745\) −35.0303 + 22.6415i −1.28341 + 0.829520i
\(746\) −0.783165 15.9772i −0.0286737 0.584966i
\(747\) 0 0
\(748\) −19.0215 15.6175i −0.695496 0.571032i
\(749\) −7.96824 + 7.96824i −0.291153 + 0.291153i
\(750\) 0 0
\(751\) 14.3204i 0.522560i −0.965263 0.261280i \(-0.915855\pi\)
0.965263 0.261280i \(-0.0841446\pi\)
\(752\) 5.40285 + 27.2239i 0.197022 + 0.992753i
\(753\) 0 0
\(754\) 4.78073 5.27357i 0.174104 0.192052i
\(755\) −6.95073 + 32.3567i −0.252963 + 1.17758i
\(756\) 0 0
\(757\) 19.9592 + 19.9592i 0.725431 + 0.725431i 0.969706 0.244275i \(-0.0785500\pi\)
−0.244275 + 0.969706i \(0.578550\pi\)
\(758\) 0.542833 + 11.0742i 0.0197166 + 0.402233i
\(759\) 0 0
\(760\) 46.2460 + 2.99465i 1.67752 + 0.108627i
\(761\) 44.8390 1.62541 0.812706 0.582674i \(-0.197994\pi\)
0.812706 + 0.582674i \(0.197994\pi\)
\(762\) 0 0
\(763\) −14.9149 + 14.9149i −0.539957 + 0.539957i
\(764\) 2.42321 + 24.6583i 0.0876687 + 0.892106i
\(765\) 0 0
\(766\) 33.5174 36.9727i 1.21103 1.33588i
\(767\) 4.36364i 0.157562i
\(768\) 0 0
\(769\) 7.94970 0.286673 0.143337 0.989674i \(-0.454217\pi\)
0.143337 + 0.989674i \(0.454217\pi\)
\(770\) 49.6927 + 8.15311i 1.79080 + 0.293818i
\(771\) 0 0
\(772\) 46.3336 4.55328i 1.66758 0.163876i
\(773\) −6.73346 + 6.73346i −0.242186 + 0.242186i −0.817754 0.575568i \(-0.804781\pi\)
0.575568 + 0.817754i \(0.304781\pi\)
\(774\) 0 0
\(775\) −3.97675 + 8.82904i −0.142849 + 0.317148i
\(776\) −41.1706 30.5550i −1.47794 1.09686i
\(777\) 0 0
\(778\) −1.02890 20.9904i −0.0368880 0.752543i
\(779\) −5.26573 + 5.26573i −0.188664 + 0.188664i
\(780\) 0 0
\(781\) −30.6605 30.6605i −1.09712 1.09712i
\(782\) 6.28931 + 5.70155i 0.224905 + 0.203887i
\(783\) 0 0
\(784\) 6.66506 1.32275i 0.238038 0.0472409i
\(785\) 17.5282 + 27.1191i 0.625608 + 0.967923i
\(786\) 0 0
\(787\) 2.03543 + 2.03543i 0.0725554 + 0.0725554i 0.742453 0.669898i \(-0.233662\pi\)
−0.669898 + 0.742453i \(0.733662\pi\)
\(788\) 1.08157 + 0.888017i 0.0385294 + 0.0316343i
\(789\) 0 0
\(790\) −0.531635 0.740326i −0.0189147 0.0263396i
\(791\) 32.7111i 1.16307i